{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 4.3 Grad-CAM++"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tensorflow Walkthrough"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. Import Dependencies"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import os\n",
    "\n",
    "from tensorflow.examples.tutorials.mnist import input_data\n",
    "from tensorflow.python.ops import nn_ops, gen_nn_ops\n",
    "import matplotlib.pyplot as plt\n",
    "import tensorflow as tf\n",
    "import numpy as np\n",
    "\n",
    "from models.models_4_3 import MNIST_CNN\n",
    "from utils import find_roi\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "mnist_cluttered = np.load('./MNIST_cluttered/mnist_sequence1_sample_5distortions5x5.npz')\n",
    "X_train = mnist_cluttered['X_train']\n",
    "y_train = mnist_cluttered['y_train']\n",
    "X_valid = mnist_cluttered['X_valid']\n",
    "y_valid = mnist_cluttered['y_valid']\n",
    "X_test = mnist_cluttered['X_test']\n",
    "y_test = mnist_cluttered['y_test']\n",
    "\n",
    "logdir = './tf_logs/4_3_GCAMPP/'\n",
    "ckptdir = logdir + 'model'\n",
    "\n",
    "if not os.path.exists(logdir):\n",
    "    os.mkdir(logdir)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Building Graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "with tf.name_scope('Classifier'):\n",
    "\n",
    "    # Initialize neural network\n",
    "    DNN = MNIST_CNN('CNN')\n",
    "\n",
    "    # Setup training process\n",
    "    X = tf.placeholder(tf.float32, [None, 1600], name='X')\n",
    "    Y = tf.placeholder(tf.int64, [None], name='Y')\n",
    "    Y_hot = tf.one_hot(Y, 10)\n",
    "\n",
    "    activations, logits = DNN(X)\n",
    "    \n",
    "    tf.add_to_collection('GCAM', X)\n",
    "    tf.add_to_collection('GCAM', logits)\n",
    "    \n",
    "    for activation in activations:\n",
    "        tf.add_to_collection('GCAM', activation)\n",
    "\n",
    "    cost = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(logits=logits, labels=Y_hot))\n",
    "\n",
    "    optimizer = tf.train.AdamOptimizer().minimize(cost, var_list=DNN.vars)\n",
    "\n",
    "    correct_prediction = tf.equal(tf.argmax(logits, 1), Y)\n",
    "    accuracy = tf.reduce_mean(tf.cast(correct_prediction, tf.float32))\n",
    "\n",
    "cost_summary = tf.summary.scalar('Cost', cost)\n",
    "accuray_summary = tf.summary.scalar('Accuracy', accuracy)\n",
    "summary = tf.summary.merge_all()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. Training Network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 0001 cost = 1.020469854 accuracy = 0.658100001\n",
      "Epoch: 0002 cost = 0.308226582 accuracy = 0.904399999\n",
      "Epoch: 0003 cost = 0.164288832 accuracy = 0.947400003\n",
      "Epoch: 0004 cost = 0.102076813 accuracy = 0.967900006\n",
      "Epoch: 0005 cost = 0.060549132 accuracy = 0.982200012\n",
      "Epoch: 0006 cost = 0.039169166 accuracy = 0.986300008\n",
      "Epoch: 0007 cost = 0.025426290 accuracy = 0.992000005\n",
      "Epoch: 0008 cost = 0.020262406 accuracy = 0.994500005\n",
      "Epoch: 0009 cost = 0.009563436 accuracy = 0.997700002\n",
      "Epoch: 0010 cost = 0.002488350 accuracy = 0.999500000\n",
      "Epoch: 0011 cost = 0.001013720 accuracy = 1.000000000\n",
      "Epoch: 0012 cost = 0.000315451 accuracy = 1.000000000\n",
      "Epoch: 0013 cost = 0.000174855 accuracy = 1.000000000\n",
      "Epoch: 0014 cost = 0.000118276 accuracy = 1.000000000\n",
      "Epoch: 0015 cost = 0.000080929 accuracy = 1.000000000\n",
      "Epoch: 0016 cost = 0.000066408 accuracy = 1.000000000\n",
      "Epoch: 0017 cost = 0.000056945 accuracy = 1.000000000\n",
      "Epoch: 0018 cost = 0.000049607 accuracy = 1.000000000\n",
      "Epoch: 0019 cost = 0.000043721 accuracy = 1.000000000\n",
      "Epoch: 0020 cost = 0.000038873 accuracy = 1.000000000\n",
      "Accuracy: 0.947\n"
     ]
    }
   ],
   "source": [
    "sess = tf.InteractiveSession()\n",
    "sess.run(tf.global_variables_initializer())\n",
    "\n",
    "saver = tf.train.Saver()\n",
    "file_writer = tf.summary.FileWriter(logdir, tf.get_default_graph())\n",
    "\n",
    "# Hyper parameters\n",
    "training_epochs = 20\n",
    "batch_size = 100\n",
    "\n",
    "for epoch in range(training_epochs):\n",
    "    total_batch = int(np.shape(X_train)[0] / batch_size)\n",
    "    avg_cost = 0\n",
    "    avg_acc = 0\n",
    "    \n",
    "    for i in range(total_batch):\n",
    "        batch_xs, batch_ys = X_train[i * batch_size:(i+1) * batch_size], y_train[i * batch_size:(i+1) * batch_size].reshape([-1])\n",
    "        _, c, a, summary_str = sess.run([optimizer, cost, accuracy, summary], feed_dict={X: batch_xs, Y: batch_ys})\n",
    "        avg_cost += c / total_batch\n",
    "        avg_acc += a / total_batch\n",
    "        \n",
    "        file_writer.add_summary(summary_str, epoch * total_batch + i)\n",
    "\n",
    "    print('Epoch:', '%04d' % (epoch + 1), 'cost =', '{:.9f}'.format(avg_cost), 'accuracy =', '{:.9f}'.format(avg_acc))\n",
    "    \n",
    "    saver.save(sess, ckptdir)\n",
    "\n",
    "print('Accuracy:', sess.run(accuracy, feed_dict={X: X_test, Y: y_test.reshape([-1])}))\n",
    "\n",
    "sess.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4. Restoring Subgraph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO:tensorflow:Restoring parameters from ./tf_logs/4_3_GCAMPP/model\n"
     ]
    }
   ],
   "source": [
    "tf.reset_default_graph()\n",
    "\n",
    "sess = tf.InteractiveSession()\n",
    "\n",
    "new_saver = tf.train.import_meta_graph(ckptdir + '.meta')\n",
    "new_saver.restore(sess, tf.train.latest_checkpoint(logdir))\n",
    "\n",
    "activations = tf.get_collection('GCAM')\n",
    "weights = tf.get_collection(tf.GraphKeys.TRAINABLE_VARIABLES, scope='.*kernel.*')\n",
    "\n",
    "X = activations[0]\n",
    "logits = activations[1]\n",
    "activations = activations[2:]\n",
    "\n",
    "sample_imgs = [X_train[y_train.reshape([-1]) == i][5] for i in range(10)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5. Generating CAMs\n",
    "\n",
    "In order to generate class activation maps, we must first calculate $\\alpha^{kc}_{ij}$ at Equation (17) of the paper. Since the gradient terms in the numerator and the denominator cancel out, we can further simplify the calculation:\n",
    "\n",
    "\\begin{equation}\n",
    "\\alpha^{kc}_{ij} = \\frac{\\left(\\frac{\\partial S^c}{\\partial A^k_{ij}}\\right)^2}{2 \\left(\\frac{\\partial S^c}{\\partial A^k_{ij}}\\right)^2 + \\sum_a \\sum_b A^k_{ab} \\left(\\frac{\\partial S^c}{\\partial A^k_{ij}}\\right)^3} = \\frac{1}{2  + \\left(\\frac{\\partial S^c}{\\partial A^k_{ij}}\\right) \\sum_a \\sum_b A^k_{ab}}\n",
    "\\end{equation}\n",
    "\n",
    "Note that the `last_conv` variable corresponds to $A^k$, `preact_grads` to $\\partial S^c / \\partial A^k$, `act_grads` to $\\partial Y^c / \\partial A^k$, `conv_sum` to $\\sum_a \\sum_b A^k_{ab}$, `alpha_kc` to $\\alpha^{kc}$ and `w_kc` to $w^c_k$ in the original paper."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "last_conv = activations[5]\n",
    "\n",
    "preact_grads = [tf.gradients(logits[:,i,None], last_conv)[0] for i in range(10)]\n",
    "act_grads = [tf.gradients(tf.exp(logits[:,i,None]), last_conv)[0] for i in range(10)]\n",
    "\n",
    "conv_sum = tf.reshape(tf.nn.avg_pool(last_conv, [1, 10, 10, 1], [1, 1, 1, 1], 'VALID') * 100, [-1,128])\n",
    "\n",
    "alpha_kc = [1 / (2 + conv_sum * preact_grad) for preact_grad in preact_grads]\n",
    "\n",
    "w_kc = [tf.nn.avg_pool(alpha_kc[i] * tf.nn.relu(act_grads[i]), [1, 10, 10, 1], [1, 1, 1, 1], 'VALID') * 100 for i in range(10)]\n",
    "\n",
    "cams = [tf.nn.relu(tf.reduce_sum(last_conv * w_kc[i], axis=3, keep_dims=True)) for i in range(10)]\n",
    "resized_cams = [tf.image.resize_bilinear(cams[i], [40,40], align_corners=True) for i in range(10)]\n",
    "\n",
    "hmaps = np.reshape([sess.run(resized_cams[i], feed_dict={X: sample_imgs[i][None]}) for i in range(10)], [10, 40, 40])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6. Displaying Images"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ZV9x+Z17cHE/mpxnOWi0OQxNTZaZuN7M9PZ/vdvfdPZ//MYDfAdDfyewpOwHsAwB3b5nZ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\niIiIiKy5/x/ECxXva7M8nQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x262b7b11eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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HFhFZC0NMTGeJ4qm6yeu1qpfX3H/dhybDIOum0CT0fpvEH8kp90T/bOhz7LEH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\njmjCOUnKivnMYXbIqnI2WPo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P7DVketvJvpJQr98iz5Ek909LzrGFroSIZMOzLSgkIiIi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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x262b7d36400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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sLvY1J4KbML1t6nDGnJs3H4ufN2PN4Gele9ppwujcqxt1nXxPkE1JJuw3RPPc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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x262b7bd9e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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JX5KzkrVZ8naaqA2SvI14rtYh7zNp6pDLa4fFXWEhmtgnJ3mbtbF8ZLYd/Sw3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\nEREphQYXIiIiIiJSiv8f6HXDKYSWASAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x262b7d3eb00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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MvI5d/y1cHzzflrMUXhZsK9Iz5vUqX6misda7QUQ0WgrbqyPMZHj3zGfOkrtuXiFYJrVs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\n4QkIERERERGNDE9AiIiIiIhoZP5/Izt5yF3FjrgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x262bae4ebe0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(5):\n",
    "    plt.figure(figsize=(15,15))\n",
    "    for j in range(2):\n",
    "        plt.subplot(5, 2, i * 2 + j + 1)\n",
    "        plt.imshow(sample_imgs[i * 2 + j].reshape(40,40), cmap='gray')\n",
    "        plt.imshow(hmaps[i * 2 + j], alpha=0.8)\n",
    "        plt.title('Digit {} Grad-CAM++'.format(i * 2 + j))\n",
    "        plt.colorbar()\n",
    "        plt.xticks([])\n",
    "        plt.yticks([])\n",
    "    plt.tight_layout()"
   ]
  },
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   "cell_type": "code",
   "execution_count": null,
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   },
   "outputs": [],
   "source": []
  }
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